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library(astsa)
library(forecast)

package ‘forecast’ was built under R version 3.4.4
Attaching package: ‘forecast’

The following object is masked from ‘package:astsa’:

    gas

X=diff(log(gnp))
plot(X)

sarima(X,1,0,0)

initial  value -4.589567 
iter   2 value -4.654150
iter   3 value -4.654150
iter   4 value -4.654151
iter   4 value -4.654151
iter   4 value -4.654151
final  value -4.654151 
converged
initial  value -4.655919 
iter   2 value -4.655921
iter   3 value -4.655922
iter   4 value -4.655922
iter   5 value -4.655922
iter   5 value -4.655922
iter   5 value -4.655922
final  value -4.655922 
converged
$fit

Call:
stats::arima(x = xdata, order = c(p, d, q), seasonal = list(order = c(P, D, 
    Q), period = S), xreg = xmean, include.mean = FALSE, transform.pars = trans, 
    fixed = fixed, optim.control = list(trace = trc, REPORT = 1, reltol = tol))

Coefficients:
         ar1   xmean
      0.3467  0.0083
s.e.  0.0627  0.0010

sigma^2 estimated as 9.03e-05:  log likelihood = 718.61,  aic = -1431.22

$degrees_of_freedom
[1] 220

$ttable
      Estimate     SE t.value p.value
ar1     0.3467 0.0627  5.5255       0
xmean   0.0083 0.0010  8.5398       0

$AIC
[1] -6.44694

$AICc
[1] -6.446693

$BIC
[1] -6.400958

plot(oil)

acf(oil); pacf(oil)

X=diff(log(oil))
layout(matrix(c(1,1,2,3), 2, 2, byrow = TRUE))
par(mar=c(4,4,1,1))

plot(X, ylab="oil price growth rate")
acf(X, 120, main=""); pacf(X, 120, main="")

auto.arima(X, seasonal=FALSE)

Series: X 
ARIMA(1,0,1) with zero mean 

Coefficients:
          ar1     ma1
      -0.5253  0.7142
s.e.   0.0872  0.0683

sigma^2 estimated as 0.002112:  log likelihood=904.58
AIC=-1803.15   AICc=-1803.11   BIC=-1790.25

out1=sarima(X,1,0,1)

initial  value -3.057594 
iter   2 value -3.061420
iter   3 value -3.067360
iter   4 value -3.067479
iter   5 value -3.071834
iter   6 value -3.074359
iter   7 value -3.074843
iter   8 value -3.076656
iter   9 value -3.080467
iter  10 value -3.081546
iter  11 value -3.081603
iter  12 value -3.081615
iter  13 value -3.081642
iter  14 value -3.081643
iter  14 value -3.081643
iter  14 value -3.081643
final  value -3.081643 
converged
initial  value -3.082345 
iter   2 value -3.082345
iter   3 value -3.082346
iter   4 value -3.082346
iter   5 value -3.082346
iter   5 value -3.082346
iter   5 value -3.082346
final  value -3.082346 
converged

ar.yw(X, 15, aic=TRUE)

Call:
ar.yw.default(x = X, aic = TRUE, order.max = 15)

Coefficients:
      1        2        3        4        5        6        7        8  
 0.1732  -0.1202   0.1804  -0.0687   0.0444  -0.0612  -0.0212   0.1207  

Order selected 8  sigma^2 estimated as  0.002075

out2=sarima(X,8,0,0)

initial  value -3.059456 
iter   2 value -3.094846
iter   3 value -3.097743
iter   4 value -3.098141
iter   5 value -3.098201
iter   6 value -3.098202
iter   7 value -3.098203
iter   8 value -3.098204
iter   9 value -3.098204
iter   9 value -3.098204
iter   9 value -3.098204
final  value -3.098204 
converged
initial  value -3.097572 
iter   2 value -3.097595
iter   3 value -3.097601
iter   4 value -3.097602
iter   5 value -3.097602
iter   6 value -3.097603
iter   7 value -3.097603
iter   7 value -3.097603
iter   7 value -3.097603
final  value -3.097603 
converged

Q3.33

plot(gtemp); acf(gtemp); pacf(gtemp)

plot(diff(gtemp)); acf(diff(gtemp)); pacf(diff(gtemp))

Q.33

p_max=q_max=7; aic = matrix( 10^(1000), p_max+1, q_max+1) 

aic

     [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,]  Inf  Inf  Inf  Inf  Inf  Inf  Inf  Inf
[2,]  Inf  Inf  Inf  Inf  Inf  Inf  Inf  Inf
[3,]  Inf  Inf  Inf  Inf  Inf  Inf  Inf  Inf
[4,]  Inf  Inf  Inf  Inf  Inf  Inf  Inf  Inf
[5,]  Inf  Inf  Inf  Inf  Inf  Inf  Inf  Inf
[6,]  Inf  Inf  Inf  Inf  Inf  Inf  Inf  Inf
[7,]  Inf  Inf  Inf  Inf  Inf  Inf  Inf  Inf
[8,]  Inf  Inf  Inf  Inf  Inf  Inf  Inf  Inf

for(p in 0:p_max){ for(q in 0:q_max){
  aic[p+1,q+1] = (sarima(gtemp,p,1,q))$AIC }}

initial  value -2.213853 
iter   1 value -2.213853
final  value -2.213853 
converged
initial  value -2.213853 
iter   1 value -2.213853
final  value -2.213853 
converged
initial  value -2.213853 
iter   2 value -2.283711
iter   3 value -2.285917
iter   4 value -2.299585
iter   5 value -2.304774
iter   6 value -2.320202
iter   7 value -2.323954
iter   8 value -2.327090
iter   9 value -2.328063
iter  10 value -2.328249
iter  11 value -2.328250
iter  12 value -2.328250
iter  13 value -2.328251
iter  14 value -2.328251
iter  14 value -2.328251
iter  14 value -2.328251
final  value -2.328251 
converged
initial  value -2.326014 
iter   2 value -2.326045
iter   3 value -2.326046
iter   4 value -2.326047
iter   5 value -2.326048
iter   5 value -2.326048
iter   5 value -2.326048
final  value -2.326048 
converged

initial  value -2.213853 
iter   2 value -2.315754
iter   3 value -2.346899
iter   4 value -2.347576
iter   5 value -2.348789
iter   6 value -2.348964
iter   7 value -2.349074
iter   8 value -2.349076
iter   8 value -2.349076
final  value -2.349076 
converged
initial  value -2.346874 
iter   2 value -2.346888
iter   3 value -2.346891
iter   4 value -2.346892
iter   5 value -2.346893
iter   5 value -2.346893
iter   5 value -2.346893
final  value -2.346893 
converged

initial  value -2.213853 
iter   2 value -2.326024
iter   3 value -2.339675
iter   4 value -2.347069
iter   5 value -2.347701
iter   6 value -2.348889
iter   7 value -2.349187
iter   8 value -2.349188
iter   8 value -2.349188
iter   8 value -2.349188
final  value -2.349188 
converged
initial  value -2.347011 
iter   2 value -2.347023
iter   3 value -2.347025
iter   4 value -2.347030
iter   5 value -2.347030
iter   5 value -2.347030
iter   5 value -2.347030
final  value -2.347030 
converged

initial  value -2.213853 
iter   2 value -2.336485
iter   3 value -2.361313
iter   4 value -2.364173
iter   5 value -2.365149
iter   6 value -2.366030
iter   7 value -2.366547
iter   8 value -2.366576
iter   9 value -2.366580
iter  10 value -2.366580
iter  10 value -2.366580
iter  10 value -2.366580
final  value -2.366580 
converged
initial  value -2.363944 
iter   2 value -2.363962
iter   3 value -2.363968
iter   4 value -2.363973
iter   5 value -2.363975
iter   6 value -2.363975
iter   6 value -2.363975
iter   6 value -2.363975
final  value -2.363975 
converged

initial  value -2.213853 
iter   2 value -2.336433
iter   3 value -2.358702
iter   4 value -2.362173
iter   5 value -2.364831
iter   6 value -2.367298
iter   7 value -2.368923
iter   8 value -2.368974
iter   9 value -2.368992
iter  10 value -2.369003
iter  11 value -2.369003
iter  12 value -2.369003
iter  12 value -2.369003
iter  12 value -2.369003
final  value -2.369003 
converged
initial  value -2.366367 
iter   2 value -2.366383
iter   3 value -2.366390
iter   4 value -2.366395
iter   5 value -2.366397
iter   6 value -2.366397
iter   6 value -2.366397
iter   6 value -2.366397
final  value -2.366397 
converged

initial  value -2.213853 
iter   2 value -2.336014
iter   3 value -2.359216
iter   4 value -2.364409
iter   5 value -2.366171
iter   6 value -2.368147
iter   7 value -2.368924
iter   8 value -2.369114
iter   9 value -2.369221
iter  10 value -2.369227
iter  11 value -2.369228
iter  11 value -2.369228
iter  11 value -2.369228
final  value -2.369228 
converged
initial  value -2.366640 
iter   2 value -2.366656
iter   3 value -2.366662
iter   4 value -2.366666
iter   5 value -2.366669
iter   6 value -2.366669
iter   7 value -2.366670
iter   7 value -2.366670
iter   7 value -2.366670
final  value -2.366670 
converged

initial  value -2.213853 
iter   2 value -2.337022
iter   3 value -2.361223
iter   4 value -2.365383
iter   5 value -2.367238
iter   6 value -2.368871
iter   7 value -2.369405
iter   8 value -2.369910
iter   9 value -2.369941
iter  10 value -2.369952
iter  11 value -2.369953
iter  12 value -2.369953
iter  12 value -2.369953
iter  12 value -2.369953
final  value -2.369953 
converged
initial  value -2.367331 
iter   2 value -2.367348
iter   3 value -2.367354
iter   4 value -2.367357
iter   5 value -2.367360
iter   6 value -2.367361
iter   6 value -2.367361
iter   6 value -2.367361
final  value -2.367361 
converged

initial  value -2.211269 
iter   2 value -2.257160
iter   3 value -2.257167
iter   4 value -2.257168
iter   4 value -2.257168
iter   4 value -2.257168
final  value -2.257168 
converged
initial  value -2.259369 
iter   2 value -2.259375
iter   3 value -2.259376
iter   3 value -2.259376
iter   3 value -2.259376
final  value -2.259376 
converged

initial  value -2.211269 
iter   2 value -2.269740
iter   3 value -2.286240
iter   4 value -2.314895
iter   5 value -2.334505
iter   6 value -2.335047
iter   7 value -2.336020
iter   8 value -2.336026
iter   9 value -2.336083
iter  10 value -2.336120
iter  11 value -2.336175
iter  12 value -2.336180
iter  12 value -2.336180
iter  12 value -2.336180
final  value -2.336180 
converged
initial  value -2.343557 
iter   2 value -2.343691
iter   3 value -2.343804
iter   4 value -2.344018
iter   5 value -2.344039
iter   6 value -2.344040
iter   6 value -2.344040
iter   6 value -2.344040
final  value -2.344040 
converged

initial  value -2.211269 
iter   2 value -2.319512
iter   3 value -2.330118
iter   4 value -2.336819
iter   5 value -2.338492
iter   6 value -2.340501
iter   7 value -2.340763
iter   8 value -2.341026
iter   9 value -2.341472
iter  10 value -2.341919
iter  11 value -2.341964
iter  12 value -2.342001
iter  13 value -2.342041
iter  14 value -2.342062
iter  15 value -2.342072
iter  16 value -2.342077
iter  17 value -2.342084
iter  18 value -2.342096
iter  19 value -2.342101
iter  20 value -2.342102
iter  21 value -2.342102
iter  22 value -2.342102
iter  22 value -2.342102
iter  22 value -2.342102
final  value -2.342102 
converged
initial  value -2.346486 
iter   2 value -2.346529
iter   3 value -2.346569
iter   4 value -2.346631
iter   5 value -2.346686
iter   6 value -2.346869
iter   7 value -2.346936
iter   8 value -2.346943
iter   9 value -2.346943
iter   9 value -2.346943
iter   9 value -2.346943
final  value -2.346943 
converged

initial  value -2.211269 
iter   2 value -2.328791
iter   3 value -2.335632
iter   4 value -2.337057
iter   5 value -2.344885
iter   6 value -2.345040
iter   7 value -2.345467
iter   8 value -2.345676
iter   9 value -2.346966
iter  10 value -2.349997
iter  11 value -2.352061
iter  12 value -2.352665
iter  13 value -2.355933
iter  14 value -2.358148
iter  15 value -2.359904
iter  16 value -2.360401
iter  17 value -2.360972
iter  18 value -2.363412
iter  19 value -2.363529
iter  20 value -2.363654
iter  21 value -2.363678
iter  22 value -2.363681
iter  22 value -2.363681
final  value -2.363681 
converged
initial  value -2.365998 
iter   2 value -2.366003
iter   3 value -2.366007
iter   4 value -2.366009
iter   5 value -2.366010
iter   5 value -2.366010
iter   5 value -2.366010
final  value -2.366010 
converged

initial  value -2.211269 
iter   2 value -2.332515
iter   3 value -2.346912
iter   4 value -2.358976
iter   5 value -2.361565
iter   6 value -2.363256
iter   7 value -2.363412
iter   8 value -2.363564
iter   9 value -2.363714
iter  10 value -2.364350
iter  11 value -2.364981
iter  12 value -2.365432
iter  13 value -2.365861
iter  14 value -2.365862
iter  15 value -2.365867
iter  16 value -2.365875
iter  17 value -2.365894
iter  18 value -2.365920
iter  19 value -2.365997
iter  20 value -2.366169
iter  21 value -2.366245
iter  22 value -2.366440
iter  23 value -2.366477
iter  24 value -2.366479
iter  25 value -2.366480
iter  26 value -2.366480
iter  26 value -2.366480
final  value -2.366480 
converged
initial  value -2.368902 
iter   2 value -2.368911
iter   3 value -2.368919
iter   4 value -2.368925
iter   5 value -2.368934
iter   6 value -2.368938
iter   7 value -2.368960
iter   8 value -2.368984
iter   9 value -2.369003
iter  10 value -2.369007
iter  11 value -2.369008
iter  11 value -2.369008
iter  11 value -2.369008
final  value -2.369008 
converged

initial  value -2.211269 
iter   2 value -2.336857
iter   3 value -2.346698
iter   4 value -2.359986
iter   5 value -2.361993
iter   6 value -2.363017
iter   7 value -2.363755
iter   8 value -2.363840
iter   9 value -2.363870
iter  10 value -2.364024
iter  11 value -2.364290
iter  12 value -2.364960
iter  13 value -2.365798
iter  14 value -2.366057
iter  15 value -2.366246
iter  16 value -2.366355
iter  17 value -2.366480
iter  18 value -2.366527
iter  19 value -2.366613
iter  20 value -2.366937
iter  21 value -2.367325
iter  22 value -2.367544
iter  23 value -2.367852
iter  24 value -2.368183
iter  25 value -2.369875
iter  26 value -2.370111
iter  27 value -2.371047
iter  28 value -2.371159
iter  29 value -2.371309
iter  30 value -2.371516
iter  31 value -2.371554
iter  32 value -2.371567
iter  33 value -2.371630
iter  34 value -2.371632
iter  35 value -2.371632
iter  35 value -2.371632
iter  35 value -2.371632
final  value -2.371632 
converged
initial  value -2.373369 
iter   2 value -2.373373
iter   3 value -2.373387
iter   4 value -2.373396
iter   5 value -2.373408
iter   6 value -2.373413
iter   7 value -2.373429
iter   8 value -2.373443
iter   9 value -2.373482
iter  10 value -2.373516
iter  11 value -2.373538
iter  12 value -2.373540
iter  13 value -2.373540
iter  13 value -2.373540
iter  13 value -2.373540
final  value -2.373540 
converged

initial  value -2.211269 
iter   2 value -2.337110
iter   3 value -2.347022
iter   4 value -2.359594
iter   5 value -2.361985
iter   6 value -2.362354
iter   7 value -2.363676
iter   8 value -2.363826
iter   9 value -2.363859
iter  10 value -2.363897
iter  11 value -2.364023
iter  12 value -2.364387
iter  13 value -2.365359
iter  14 value -2.365773
iter  15 value -2.365879
iter  16 value -2.366098
iter  17 value -2.366655
iter  18 value -2.366813
iter  19 value -2.366929
iter  20 value -2.367066
iter  21 value -2.367132
iter  22 value -2.367766
iter  23 value -2.368799
iter  24 value -2.369855
iter  25 value -2.370251
iter  26 value -2.370920
iter  27 value -2.371602
iter  28 value -2.371777
iter  29 value -2.371825
iter  30 value -2.371830
iter  31 value -2.371831
iter  31 value -2.371831
final  value -2.371831 
converged
initial  value -2.373567 
iter   2 value -2.373575
iter   3 value -2.373591
iter   4 value -2.373601
iter   5 value -2.373613
iter   6 value -2.373621
iter   7 value -2.373641
iter   8 value -2.373668
iter   9 value -2.373717
iter  10 value -2.373777
iter  11 value -2.373816
iter  12 value -2.373824
iter  13 value -2.373826
iter  14 value -2.373826
iter  15 value -2.373826
iter  15 value -2.373826
iter  15 value -2.373826
final  value -2.373826 
converged

initial  value -2.211269 
iter   2 value -2.338461
iter   3 value -2.348519
iter   4 value -2.360456
iter   5 value -2.362876
iter   6 value -2.363635
iter   7 value -2.364135
iter   8 value -2.364271
iter   9 value -2.364292
iter  10 value -2.364308
iter  11 value -2.364375
iter  12 value -2.364531
iter  13 value -2.364873
iter  14 value -2.370151
iter  15 value -2.370392
iter  16 value -2.370848
iter  17 value -2.371021
iter  18 value -2.371736
iter  19 value -2.371927
iter  20 value -2.372016
iter  21 value -2.372105
iter  22 value -2.372143
iter  23 value -2.372150
iter  24 value -2.372152
iter  24 value -2.372152
iter  24 value -2.372152
final  value -2.372152 
converged
initial  value -2.373759 
iter   2 value -2.373764
iter   3 value -2.373777
iter   4 value -2.373785
iter   5 value -2.373802
iter   6 value -2.373814
iter   7 value -2.373826
iter   8 value -2.373833
iter   9 value -2.373849
iter  10 value -2.373871
iter  11 value -2.373905
iter  12 value -2.373938
iter  13 value -2.373956
iter  14 value -2.373960
iter  15 value -2.373962
iter  16 value -2.373962
iter  16 value -2.373962
iter  16 value -2.373962
final  value -2.373962 
converged

initial  value -2.208390 
iter   2 value -2.285072
iter   3 value -2.292165
iter   4 value -2.293106
iter   5 value -2.293131
iter   6 value -2.293145
iter   7 value -2.293145
iter   7 value -2.293145
iter   7 value -2.293145
final  value -2.293145 
converged
initial  value -2.298164 
iter   2 value -2.298170
iter   3 value -2.298170
iter   4 value -2.298170
iter   4 value -2.298170
iter   4 value -2.298170
final  value -2.298170 
converged

initial  value -2.208390 
iter   2 value -2.299355
iter   3 value -2.318238
iter   4 value -2.321848
iter   5 value -2.334754
iter   6 value -2.340159
iter   7 value -2.343356
iter   8 value -2.347022
iter   9 value -2.347677
iter  10 value -2.348030
iter  11 value -2.348038
iter  12 value -2.348041
iter  13 value -2.348046
iter  14 value -2.348050
iter  14 value -2.348050
iter  14 value -2.348050
final  value -2.348050 
converged
initial  value -2.350024 
iter   2 value -2.350046
iter   3 value -2.350063
iter   4 value -2.350078
iter   5 value -2.350083
iter   6 value -2.350085
iter   6 value -2.350085
iter   6 value -2.350085
final  value -2.350085 
converged

initial  value -2.208390 
iter   2 value -2.326583
iter   3 value -2.332136
iter   4 value -2.334357
iter   5 value -2.336577
iter   6 value -2.341490
iter   7 value -2.341948
iter   8 value -2.342190
iter   9 value -2.342445
iter  10 value -2.343536
iter  11 value -2.345244
iter  12 value -2.346658
iter  13 value -2.348139
iter  14 value -2.348560
iter  15 value -2.348922
iter  16 value -2.349161
iter  17 value -2.349254
iter  18 value -2.349376
iter  19 value -2.349661
iter  20 value -2.350269
iter  21 value -2.351235
iter  22 value -2.351439
iter  23 value -2.351508
iter  24 value -2.351512
iter  25 value -2.351523
iter  26 value -2.351524
iter  27 value -2.351524
iter  28 value -2.351525
iter  29 value -2.351525
iter  30 value -2.351525
iter  31 value -2.351526
iter  32 value -2.351527
iter  33 value -2.351527
iter  34 value -2.351527
iter  34 value -2.351527
final  value -2.351527 
converged
initial  value -2.351237 
iter   2 value -2.351316
iter   3 value -2.351423
iter   4 value -2.351435
iter   5 value -2.351446
iter   6 value -2.351451
iter   7 value -2.351453
iter   8 value -2.351457
iter   9 value -2.351461
iter  10 value -2.351472
iter  11 value -2.351488
iter  12 value -2.351511
iter  13 value -2.351512
iter  14 value -2.351517
iter  15 value -2.351520
iter  16 value -2.351523
iter  17 value -2.351524
iter  18 value -2.351524
iter  19 value -2.351525
iter  20 value -2.351526
iter  21 value -2.351527
iter  22 value -2.351529
iter  23 value -2.351529
iter  23 value -2.351529
final  value -2.351529 
converged

initial  value -2.208390 
iter   2 value -2.343075
iter   3 value -2.347906
iter   4 value -2.348386
iter   5 value -2.349240
iter   6 value -2.350358
iter   7 value -2.351032
iter   8 value -2.352496
iter   9 value -2.355590
iter  10 value -2.358731
iter  11 value -2.360776
iter  12 value -2.362231
iter  13 value -2.362819
iter  14 value -2.363139
iter  15 value -2.363203
iter  16 value -2.363235
iter  17 value -2.363275
iter  18 value -2.363303
iter  19 value -2.363326
iter  20 value -2.363341
iter  21 value -2.363355
iter  22 value -2.363361
iter  23 value -2.363369
iter  24 value -2.363378
iter  25 value -2.363382
iter  26 value -2.363383
iter  26 value -2.363383
iter  26 value -2.363383
final  value -2.363383 
converged
initial  value -2.371896 
iter   2 value -2.372019
iter   3 value -2.372139
iter   4 value -2.372446
iter   5 value -2.372619
iter   6 value -2.372942
iter   7 value -2.372998
iter   8 value -2.373003
iter   9 value -2.373004
iter  10 value -2.373004
iter  11 value -2.373004
iter  12 value -2.373004
iter  12 value -2.373004
iter  12 value -2.373004
final  value -2.373004 
converged

initial  value -2.208390 
iter   2 value -2.341161
iter   3 value -2.351921
iter   4 value -2.358232
iter   5 value -2.360938
iter   6 value -2.362005
iter   7 value -2.362885
iter   8 value -2.362935
iter   9 value -2.363046
iter  10 value -2.363554
iter  11 value -2.363664
iter  12 value -2.363694
iter  13 value -2.363694
iter  14 value -2.363695
iter  15 value -2.363695
iter  16 value -2.363696
iter  17 value -2.363697
iter  18 value -2.363697
iter  19 value -2.363697
iter  20 value -2.363697
iter  21 value -2.363698
iter  22 value -2.363699
iter  23 value -2.363703
iter  24 value -2.363710
iter  25 value -2.363717
iter  26 value -2.363720
iter  27 value -2.363721
iter  28 value -2.363721
iter  29 value -2.363721
iter  30 value -2.363721
iter  31 value -2.363722
iter  32 value -2.363722
iter  33 value -2.363722
iter  33 value -2.363722
iter  33 value -2.363722
final  value -2.363722 
converged
initial  value -2.366494 
iter   2 value -2.366525
iter   3 value -2.366567
iter   4 value -2.366574
iter   5 value -2.366600
iter   6 value -2.366613
iter   7 value -2.366638
iter   8 value -2.366863
iter   9 value -2.367047
iter  10 value -2.367195
iter  11 value -2.367485
iter  12 value -2.368327
iter  13 value -2.370191
iter  14 value -2.370637
iter  15 value -2.370651
iter  16 value -2.370688
iter  17 value -2.370693
iter  18 value -2.370697
iter  19 value -2.370700
iter  20 value -2.370704
iter  21 value -2.370705
iter  22 value -2.370708
iter  23 value -2.370717
iter  24 value -2.370719
iter  25 value -2.370720
iter  25 value -2.370720
iter  25 value -2.370720
final  value -2.370720 
converged

initial  value -2.208390 
iter   2 value -2.346335
iter   3 value -2.352657
iter   4 value -2.357542
iter   5 value -2.361408
iter   6 value -2.363374
iter   7 value -2.363703
iter   8 value -2.363745
iter   9 value -2.363757
iter  10 value -2.363768
iter  11 value -2.363847
iter  12 value -2.363951
iter  13 value -2.364077
iter  14 value -2.364169
iter  15 value -2.364209
iter  16 value -2.364225
iter  17 value -2.364260
iter  18 value -2.364344
iter  19 value -2.364354
iter  20 value -2.364355
iter  21 value -2.364375
iter  22 value -2.364379
iter  23 value -2.364389
iter  24 value -2.364467
iter  25 value -2.364709
iter  26 value -2.365102
iter  27 value -2.365838
iter  28 value -2.366895
iter  29 value -2.367174
iter  30 value -2.367227
iter  31 value -2.367502
iter  32 value -2.367561
iter  33 value -2.367623
iter  34 value -2.368053
iter  35 value -2.368503
iter  36 value -2.370300
iter  37 value -2.370320
iter  38 value -2.371166
iter  39 value -2.373574
iter  40 value -2.377391
iter  41 value -2.378857
iter  42 value -2.381465
iter  43 value -2.382684
iter  44 value -2.383576
iter  45 value -2.386984
iter  46 value -2.388552
iter  47 value -2.392878
iter  48 value -2.396077
iter  49 value -2.398191
iter  50 value -2.409204
iter  51 value -2.409720
iter  52 value -2.410899
iter  53 value -2.411013
iter  54 value -2.411149
iter  55 value -2.412477
iter  56 value -2.413107
iter  57 value -2.413936
iter  57 value -2.413936
iter  58 value -2.414012
iter  58 value -2.414012
iter  59 value -2.414030
iter  59 value -2.414030
iter  60 value -2.414030
iter  60 value -2.414030
iter  60 value -2.414030
final  value -2.414030 
converged
initial  value -2.362138 
iter   2 value -2.364390
iter   3 value -2.365266
iter   4 value -2.366931
iter   5 value -2.368238
iter   6 value -2.368480
iter   7 value -2.368650
iter   8 value -2.368793
iter   9 value -2.368948
iter  10 value -2.369160
iter  11 value -2.369379
iter  12 value -2.369489
iter  13 value -2.369508
iter  14 value -2.369511
iter  15 value -2.369513
iter  16 value -2.369514
iter  17 value -2.369517
iter  18 value -2.369526
iter  19 value -2.369528
iter  20 value -2.369532
iter  21 value -2.369534
iter  22 value -2.369535
iter  23 value -2.369537
iter  24 value -2.369539
iter  25 value -2.369550
iter  26 value -2.369585
iter  27 value -2.369652
iter  28 value -2.369709
iter  29 value -2.369717
iter  30 value -2.369727
iter  31 value -2.369733
iter  32 value -2.369755
iter  33 value -2.369789
iter  34 value -2.369899
iter  35 value -2.370128
iter  36 value -2.370169
iter  37 value -2.370274
iter  38 value -2.370667
iter  39 value -2.370895
iter  40 value -2.371156
iter  41 value -2.371213
iter  42 value -2.371228
iter  43 value -2.371245
iter  44 value -2.371257
iter  45 value -2.371283
iter  46 value -2.371322
iter  47 value -2.371380
iter  48 value -2.371437
iter  49 value -2.371473
iter  50 value -2.371478
iter  51 value -2.371481
iter  52 value -2.371489
iter  53 value -2.371489
iter  54 value -2.371490
iter  55 value -2.371492
iter  56 value -2.371497
iter  57 value -2.371500
iter  58 value -2.371506
iter  59 value -2.371517
iter  60 value -2.371528
iter  61 value -2.371534
iter  62 value -2.371535
iter  63 value -2.371535
iter  64 value -2.371536
iter  65 value -2.371537
iter  66 value -2.371540
iter  67 value -2.371543
iter  68 value -2.371545
iter  69 value -2.371545
iter  69 value -2.371545
final  value -2.371545 
converged

initial  value -2.208390 
iter   2 value -2.346792
iter   3 value -2.353167
iter   4 value -2.354543
iter   5 value -2.358587
iter   6 value -2.361838
iter   7 value -2.363804
iter   8 value -2.364050
iter   9 value -2.364096
iter  10 value -2.364104
iter  11 value -2.364111
iter  12 value -2.364170
iter  13 value -2.364349
iter  14 value -2.364553
iter  15 value -2.364912
iter  16 value -2.365409
iter  17 value -2.366432
iter  18 value -2.366771
iter  19 value -2.366773
iter  20 value -2.367327
iter  21 value -2.367462
iter  22 value -2.367612
iter  23 value -2.367832
iter  24 value -2.368046
iter  25 value -2.368080
iter  26 value -2.368132
iter  27 value -2.368160
iter  28 value -2.368230
iter  29 value -2.368294
iter  30 value -2.368359
iter  31 value -2.368404
iter  32 value -2.368437
iter  33 value -2.368439
iter  34 value -2.368440
iter  35 value -2.368441
iter  36 value -2.368444
iter  37 value -2.368448
iter  38 value -2.368456
iter  39 value -2.368463
iter  40 value -2.368464
iter  41 value -2.368464
iter  42 value -2.368465
iter  43 value -2.368466
iter  44 value -2.368466
iter  45 value -2.368467
iter  45 value -2.368467
iter  45 value -2.368467
final  value -2.368467 
converged
initial  value -2.366448 
iter   2 value -2.366629
iter   3 value -2.366680
iter   4 value -2.366765
iter   5 value -2.366814
iter   6 value -2.366852
iter   7 value -2.366859
iter   8 value -2.366862
iter   9 value -2.366865
iter  10 value -2.366875
iter  11 value -2.366905
iter  12 value -2.366930
iter  13 value -2.366976
iter  14 value -2.367027
iter  15 value -2.367217
iter  16 value -2.367722
iter  17 value -2.367768
iter  18 value -2.367835
iter  19 value -2.367978
iter  20 value -2.368047
iter  21 value -2.368051
iter  22 value -2.368054
iter  23 value -2.368056
iter  24 value -2.368057
iter  25 value -2.368058
iter  26 value -2.368064
iter  27 value -2.368068
iter  28 value -2.368079
iter  29 value -2.368090
iter  30 value -2.368106
iter  31 value -2.368122
iter  32 value -2.368128
iter  33 value -2.368131
iter  34 value -2.368132
iter  35 value -2.368134
iter  36 value -2.368137
iter  37 value -2.368146
iter  38 value -2.368179
iter  39 value -2.368188
iter  40 value -2.368360
iter  41 value -2.368429
iter  42 value -2.368563
iter  43 value -2.368609
iter  44 value -2.368643
iter  45 value -2.368664
iter  46 value -2.368686
iter  47 value -2.368758
iter  48 value -2.370614
iter  49 value -2.370696
iter  50 value -2.371479
iter  51 value -2.373541
iter  52 value -2.375832
iter  53 value -2.377687
iter  54 value -2.378099
iter  55 value -2.378514
iter  56 value -2.379130
iter  57 value -2.381660
iter  58 value -2.381729
iter  59 value -2.386190
iter  60 value -2.386604
iter  61 value -2.388347
iter  62 value -2.388820
iter  63 value -2.389580
iter  64 value -2.389696
iter  65 value -2.389893
iter  66 value -2.389939
iter  67 value -2.389956
iter  68 value -2.389964
iter  69 value -2.389971
iter  70 value -2.389978
iter  71 value -2.389984
iter  72 value -2.389987
iter  73 value -2.389990
iter  74 value -2.389991
iter  75 value -2.389991
iter  75 value -2.389991
iter  75 value -2.389991
final  value -2.389991 
converged

initial  value -2.208390 
iter   2 value -2.348265
iter   3 value -2.350551
iter   4 value -2.357509
iter   5 value -2.360503
iter   6 value -2.361356
iter   7 value -2.364515
iter   8 value -2.364649
iter   9 value -2.364688
iter  10 value -2.364703
iter  11 value -2.364723
iter  12 value -2.364779
iter  13 value -2.364923
iter  14 value -2.365187
iter  15 value -2.365856
iter  16 value -2.366707
iter  17 value -2.366873
iter  18 value -2.367358
iter  19 value -2.368050
iter  20 value -2.368261
iter  21 value -2.368318
iter  22 value -2.368434
iter  23 value -2.368436
iter  24 value -2.368436
iter  25 value -2.368445
iter  26 value -2.368456
iter  27 value -2.368457
iter  28 value -2.368460
iter  29 value -2.368461
iter  30 value -2.368463
iter  31 value -2.368463
iter  32 value -2.368464
iter  33 value -2.368465
iter  34 value -2.368465
iter  35 value -2.368465
iter  36 value -2.368465
iter  37 value -2.368465
iter  38 value -2.368465
iter  39 value -2.368466
iter  40 value -2.368466
iter  41 value -2.368467
iter  42 value -2.368468
iter  43 value -2.368468
iter  43 value -2.368468
final  value -2.368468 
converged
initial  value -2.366470 
iter   2 value -2.366533
iter   3 value -2.366572
iter   4 value -2.366622
iter   5 value -2.366710
iter   6 value -2.366821
iter   7 value -2.366879
iter   8 value -2.366882
iter   9 value -2.366887
iter  10 value -2.366894
iter  11 value -2.366906
iter  12 value -2.366953
iter  13 value -2.367012
iter  14 value -2.367047
iter  15 value -2.367125
iter  16 value -2.367386
iter  17 value -2.367950
iter  18 value -2.368025
iter  19 value -2.368056
iter  20 value -2.368080
iter  21 value -2.368089
iter  22 value -2.368096
iter  23 value -2.368098
iter  24 value -2.368098
iter  25 value -2.368100
iter  26 value -2.368100
iter  27 value -2.368101
iter  28 value -2.368101
iter  29 value -2.368101
iter  30 value -2.368102
iter  31 value -2.368103
iter  32 value -2.368106
iter  33 value -2.368112
iter  34 value -2.368137
iter  35 value -2.368158
iter  36 value -2.368167
iter  37 value -2.368191
iter  38 value -2.368237
iter  39 value -2.368286
iter  40 value -2.368529
iter  41 value -2.369395
iter  42 value -2.369736
iter  43 value -2.369931
iter  44 value -2.370030
iter  45 value -2.370090
iter  46 value -2.370163
iter  47 value -2.370298
iter  48 value -2.370543
iter  49 value -2.371686
iter  50 value -2.372503
iter  51 value -2.373020
iter  52 value -2.374298
iter  53 value -2.376755
iter  54 value -2.377562
iter  55 value -2.380797
iter  56 value -2.381347
iter  57 value -2.383089
iter  58 value -2.383946
iter  59 value -2.385161
iter  60 value -2.386070
iter  61 value -2.387782
iter  62 value -2.388882
iter  63 value -2.390052
iter  64 value -2.391221
iter  65 value -2.391873
iter  66 value -2.392133
iter  67 value -2.392423
iter  68 value -2.392750
iter  69 value -2.392773
iter  70 value -2.393165
iter  71 value -2.393238
iter  72 value -2.393340
iter  73 value -2.393808
iter  74 value -2.393932
iter  75 value -2.394094
iter  76 value -2.394158
iter  77 value -2.394243
iter  78 value -2.394292
iter  79 value -2.394465
iter  80 value -2.394720
iter  81 value -2.394852
iter  82 value -2.395047
iter  83 value -2.395371
iter  84 value -2.396133
iter  85 value -2.396355
iter  86 value -2.396518
iter  87 value -2.396619
iter  88 value -2.396626
iter  89 value -2.396627
iter  90 value -2.396627
iter  90 value -2.396627
iter  90 value -2.396627
final  value -2.396627 
converged

initial  value -2.204527 
iter   2 value -2.305202
iter   3 value -2.330608
iter   4 value -2.340780
iter   5 value -2.342247
iter   6 value -2.342618
iter   7 value -2.342622
iter   8 value -2.342622
iter   8 value -2.342622
iter   8 value -2.342622
final  value -2.342622 
converged
initial  value -2.350196 
iter   2 value -2.350213
iter   3 value -2.350218
iter   4 value -2.350218
iter   5 value -2.350220
iter   6 value -2.350220
iter   6 value -2.350220
iter   6 value -2.350220
final  value -2.350220 
converged

initial  value -2.204527 
iter   2 value -2.320466
iter   3 value -2.340026
iter   4 value -2.342073
iter   5 value -2.343602
iter   6 value -2.344256
iter   7 value -2.344340
iter   8 value -2.344683
iter   9 value -2.345686
iter  10 value -2.346309
iter  11 value -2.347424
iter  12 value -2.347474
iter  13 value -2.347475
iter  14 value -2.347475
iter  15 value -2.347476
iter  16 value -2.347476
iter  16 value -2.347476
iter  16 value -2.347476
final  value -2.347476 
converged
initial  value -2.353882 
iter   2 value -2.353904
iter   3 value -2.353915
iter   4 value -2.353922
iter   5 value -2.353925
iter   6 value -2.353934
iter   7 value -2.353935
iter   8 value -2.353935
iter   8 value -2.353935
iter   8 value -2.353935
final  value -2.353935 
converged

initial  value -2.204527 
iter   2 value -2.344219
iter   3 value -2.351485
iter   4 value -2.352337
iter   5 value -2.353102
iter   6 value -2.353852
iter   7 value -2.354414
iter   8 value -2.356923
iter   9 value -2.358764
iter  10 value -2.361114
iter  11 value -2.361887
iter  12 value -2.362688
iter  13 value -2.363217
iter  14 value -2.364296
iter  15 value -2.364345
iter  16 value -2.365060
iter  17 value -2.365432
iter  18 value -2.366112
iter  19 value -2.366364
iter  20 value -2.366399
iter  21 value -2.366422
iter  22 value -2.366433
iter  23 value -2.366436
iter  24 value -2.366437
iter  24 value -2.366437
iter  24 value -2.366437
final  value -2.366437 
converged
initial  value -2.371682 
iter   2 value -2.371709
iter   3 value -2.371738
iter   4 value -2.371754
iter   5 value -2.371764
iter   6 value -2.371769
iter   7 value -2.371774
iter   8 value -2.371779
iter   9 value -2.371781
iter  10 value -2.371792
iter  11 value -2.371801
iter  12 value -2.371807
iter  13 value -2.371808
iter  14 value -2.371808
iter  14 value -2.371808
final  value -2.371808 
converged

initial  value -2.204527 
iter   2 value -2.347539
iter   3 value -2.349760
iter   4 value -2.351034
iter   5 value -2.352886
iter   6 value -2.353689
iter   7 value -2.354132
iter   8 value -2.354680
iter   9 value -2.357442
iter  10 value -2.358660
iter  11 value -2.360846
iter  12 value -2.361830
iter  13 value -2.363278
iter  14 value -2.363794
iter  15 value -2.364971
iter  16 value -2.365887
iter  17 value -2.365946
iter  18 value -2.366053
iter  19 value -2.366112
iter  20 value -2.366279
iter  21 value -2.366396
iter  22 value -2.366466
iter  23 value -2.366476
iter  24 value -2.366486
iter  25 value -2.366491
iter  26 value -2.366499
iter  27 value -2.366511
iter  28 value -2.366530
iter  29 value -2.366544
iter  30 value -2.366548
iter  31 value -2.366548
iter  31 value -2.366548
final  value -2.366548 
converged
initial  value -2.372124 
iter   2 value -2.372161
iter   3 value -2.372177
iter   4 value -2.372183
iter   5 value -2.372206
iter   6 value -2.372248
iter   7 value -2.372309
iter   8 value -2.372362
iter   9 value -2.372390
iter  10 value -2.372394
iter  11 value -2.372395
iter  12 value -2.372396
iter  13 value -2.372397
iter  14 value -2.372397
iter  15 value -2.372398
iter  16 value -2.372400
iter  17 value -2.372401
iter  18 value -2.372401
iter  19 value -2.372402
iter  20 value -2.372402
iter  21 value -2.372402
iter  22 value -2.372402
iter  23 value -2.372402
iter  24 value -2.372403
iter  25 value -2.372403
iter  26 value -2.372403
iter  27 value -2.372403
iter  27 value -2.372403
iter  27 value -2.372403
final  value -2.372403 
converged

initial  value -2.204527 
iter   2 value -2.340086
iter   3 value -2.350272
iter   4 value -2.354145
iter   5 value -2.357161
iter   6 value -2.358340
iter   7 value -2.359109
iter   8 value -2.359442
iter   9 value -2.360083
iter  10 value -2.360514
iter  11 value -2.360688
iter  12 value -2.360751
iter  13 value -2.360885
iter  14 value -2.361237
iter  15 value -2.364013
iter  16 value -2.364151
iter  17 value -2.365592
iter  18 value -2.367271
iter  19 value -2.367410
iter  20 value -2.367486
iter  21 value -2.367561
iter  22 value -2.367602
iter  23 value -2.367624
iter  24 value -2.367662
iter  25 value -2.367719
iter  26 value -2.367849
iter  27 value -2.367931
iter  28 value -2.367966
iter  29 value -2.367974
iter  30 value -2.367974
iter  31 value -2.367975
iter  32 value -2.367976
iter  33 value -2.367976
iter  34 value -2.367977
iter  35 value -2.367978
iter  36 value -2.367978
iter  37 value -2.367979
iter  38 value -2.367979
iter  39 value -2.367979
iter  40 value -2.367979
iter  41 value -2.367980
iter  42 value -2.367980
iter  43 value -2.367980
iter  44 value -2.367981
iter  45 value -2.367981
iter  46 value -2.367982
iter  47 value -2.367982
iter  48 value -2.367982
iter  49 value -2.367982
iter  50 value -2.367982
iter  51 value -2.367982
iter  52 value -2.367982
iter  52 value -2.367982
final  value -2.367982 
converged
initial  value -2.370233 
iter   2 value -2.370374
iter   3 value -2.370429
iter   4 value -2.370465
iter   5 value -2.370483
iter   6 value -2.370532
iter   7 value -2.370566
iter   8 value -2.370720
iter   9 value -2.370967
iter  10 value -2.371137
iter  11 value -2.371283
iter  12 value -2.371297
iter  13 value -2.371308
iter  14 value -2.371336
iter  15 value -2.371381
iter  16 value -2.371421
iter  17 value -2.371439
iter  18 value -2.371454
iter  19 value -2.371462
iter  20 value -2.371472
iter  21 value -2.371508
iter  22 value -2.371544
iter  23 value -2.371567
iter  24 value -2.371572
iter  25 value -2.371577
iter  26 value -2.371583
iter  27 value -2.371618
iter  28 value -2.371654
iter  29 value -2.371689
iter  30 value -2.371708
iter  31 value -2.371712
iter  32 value -2.371719
iter  33 value -2.371743
iter  34 value -2.371814
iter  35 value -2.371835
iter  36 value -2.372226
iter  37 value -2.372371
iter  38 value -2.372453
iter  39 value -2.372522
iter  40 value -2.372823
iter  41 value -2.373272
iter  42 value -2.374421
iter  43 value -2.374935
iter  44 value -2.375810
iter  45 value -2.376842
iter  46 value -2.377600
iter  47 value -2.379255
iter  48 value -2.379867
iter  49 value -2.380169
iter  50 value -2.380523
iter  51 value -2.381145
iter  52 value -2.381496
iter  53 value -2.381531
iter  54 value -2.381576
iter  55 value -2.381614
iter  56 value -2.381642
iter  57 value -2.381695
iter  58 value -2.381803
iter  59 value -2.381938
iter  60 value -2.382102
iter  61 value -2.382192
iter  62 value -2.382230
iter  63 value -2.382301
iter  64 value -2.382382
iter  65 value -2.382425
iter  66 value -2.382459
iter  67 value -2.382476
iter  68 value -2.382493
iter  69 value -2.382499
iter  70 value -2.382500
iter  71 value -2.382503
iter  72 value -2.382505
iter  73 value -2.382506
iter  74 value -2.382506
iter  75 value -2.382507
iter  76 value -2.382507
iter  77 value -2.382508
iter  78 value -2.382508
iter  79 value -2.382508
iter  80 value -2.382508
iter  81 value -2.382509
iter  82 value -2.382509
iter  83 value -2.382510
iter  84 value -2.382510
iter  85 value -2.382510
iter  86 value -2.382510
iter  86 value -2.382510
final  value -2.382510 
converged

initial  value -2.204527 
iter   2 value -2.345953
iter   3 value -2.356935
iter   4 value -2.357660
iter   5 value -2.359106
iter   6 value -2.359890
iter   7 value -2.360401
iter   8 value -2.360442
iter   9 value -2.360488
iter  10 value -2.361024
iter  11 value -2.362619
iter  12 value -2.363326
iter  13 value -2.363664
iter  14 value -2.364006
iter  15 value -2.364358
iter  16 value -2.364642
iter  17 value -2.364889
iter  18 value -2.365644
iter  19 value -2.365946
iter  20 value -2.366719
iter  21 value -2.367010
iter  22 value -2.367447
iter  23 value -2.367519
iter  24 value -2.367528
iter  25 value -2.367564
iter  26 value -2.367603
iter  27 value -2.367635
iter  28 value -2.367708
iter  29 value -2.367739
iter  30 value -2.367749
iter  31 value -2.367761
iter  32 value -2.367768
iter  33 value -2.367956
iter  34 value -2.367982
iter  35 value -2.367996
iter  36 value -2.368002
iter  37 value -2.368010
iter  38 value -2.368020
iter  39 value -2.368050
iter  40 value -2.368053
iter  41 value -2.368061
iter  42 value -2.368074
iter  43 value -2.368093
iter  44 value -2.368098
iter  45 value -2.368108
iter  46 value -2.368116
iter  47 value -2.368136
iter  48 value -2.368155
iter  49 value -2.368184
iter  50 value -2.368212
iter  51 value -2.368265
iter  52 value -2.368286
iter  53 value -2.368289
iter  54 value -2.368295
iter  55 value -2.368318
iter  56 value -2.368359
iter  57 value -2.368429
iter  58 value -2.368475
iter  59 value -2.368478
iter  60 value -2.368490
iter  61 value -2.368492
iter  62 value -2.368494
iter  63 value -2.368498
iter  64 value -2.368500
iter  65 value -2.368509
iter  66 value -2.368520
iter  67 value -2.368521
iter  68 value -2.368521
iter  68 value -2.368521
iter  68 value -2.368521
final  value -2.368521 
converged
initial  value -2.370506 
iter   2 value -2.370632
iter   3 value -2.370713
iter   4 value -2.370753
iter   5 value -2.370783
iter   6 value -2.370820
iter   7 value -2.370833
iter   8 value -2.370861
iter   9 value -2.370930
iter  10 value -2.371008
iter  11 value -2.371054
iter  12 value -2.371068
iter  13 value -2.371069
iter  14 value -2.371069
iter  15 value -2.371072
iter  16 value -2.371076
iter  17 value -2.371081
iter  18 value -2.371084
iter  19 value -2.371084
iter  20 value -2.371085
iter  20 value -2.371085
final  value -2.371085 
converged

initial  value -2.204527 
iter   2 value -2.346054
iter   3 value -2.357018
iter   4 value -2.358475
iter   5 value -2.359911
iter   6 value -2.360558
iter   7 value -2.360834
iter   8 value -2.360852
iter   9 value -2.360863
iter  10 value -2.360928
iter  11 value -2.361097
iter  12 value -2.361305
iter  13 value -2.362083
iter  14 value -2.364239
iter  15 value -2.364410
iter  16 value -2.364809
iter  17 value -2.364979
iter  18 value -2.365124
iter  19 value -2.365317
iter  20 value -2.365492
iter  21 value -2.365956
iter  22 value -2.367966
iter  23 value -2.368333
iter  24 value -2.368425
iter  25 value -2.369291
iter  26 value -2.369997
iter  27 value -2.370003
iter  28 value -2.370239
iter  29 value -2.370311
iter  30 value -2.370500
iter  31 value -2.370738
iter  32 value -2.370883
iter  33 value -2.370961
iter  34 value -2.370982
iter  35 value -2.371007
iter  36 value -2.371009
iter  37 value -2.371016
iter  38 value -2.371024
iter  39 value -2.371036
iter  40 value -2.371045
iter  41 value -2.371071
iter  42 value -2.371117
iter  43 value -2.371251
iter  44 value -2.371426
iter  45 value -2.371595
iter  46 value -2.371649
iter  47 value -2.371664
iter  48 value -2.371671
iter  49 value -2.371688
iter  50 value -2.371709
iter  51 value -2.371729
iter  52 value -2.371737
iter  53 value -2.371739
iter  54 value -2.371739
iter  54 value -2.371739
iter  54 value -2.371739
final  value -2.371739 
converged
initial  value -2.373222 
iter   2 value -2.373277
iter   3 value -2.373369
iter   4 value -2.373474
iter   5 value -2.373497
iter   6 value -2.373558
iter   7 value -2.373617
iter   8 value -2.373654
iter   9 value -2.373659
iter  10 value -2.373687
iter  11 value -2.373711
iter  12 value -2.373736
iter  13 value -2.373747
iter  14 value -2.373749
iter  15 value -2.373749
iter  15 value -2.373749
iter  15 value -2.373749
final  value -2.373749 
converged

initial  value -2.204527 
iter   2 value -2.347367
iter   3 value -2.358944
iter   4 value -2.360313
iter   5 value -2.361262
iter   6 value -2.361673
iter   7 value -2.361882
iter   8 value -2.361911
iter   9 value -2.361946
iter  10 value -2.362161
iter  11 value -2.362828
iter  12 value -2.365408
iter  13 value -2.366492
iter  14 value -2.366800
iter  15 value -2.367185
iter  16 value -2.367717
iter  17 value -2.368272
iter  18 value -2.369004
iter  19 value -2.369350
iter  20 value -2.370452
iter  21 value -2.371731
iter  22 value -2.371778
iter  23 value -2.372168
iter  24 value -2.372315
iter  25 value -2.372403
iter  26 value -2.372504
iter  27 value -2.372735
iter  28 value -2.373034
iter  29 value -2.373090
iter  30 value -2.373129
iter  31 value -2.373157
iter  32 value -2.373252
iter  33 value -2.373476
iter  34 value -2.373735
iter  35 value -2.374052
iter  36 value -2.374768
iter  37 value -2.374903
iter  38 value -2.375002
iter  39 value -2.375202
iter  40 value -2.375289
iter  41 value -2.375358
iter  42 value -2.375416
iter  43 value -2.375431
iter  44 value -2.375479
iter  45 value -2.375614
iter  46 value -2.376144
iter  47 value -2.376216
iter  48 value -2.376712
iter  49 value -2.376911
iter  50 value -2.377864
iter  51 value -2.379360
iter  52 value -2.381835
iter  53 value -2.383483
iter  54 value -2.384224
iter  55 value -2.385707
iter  56 value -2.386339
iter  57 value -2.390828
iter  58 value -2.395359
iter  59 value -2.398732
iter  60 value -2.404072
iter  61 value -2.404077
iter  62 value -2.407820
iter  63 value -2.410445
iter  64 value -2.417088
iter  65 value -2.422547
iter  66 value -2.426360
iter  67 value -2.428895
iter  68 value -2.430379
iter  69 value -2.436179
iter  70 value -2.437362
iter  71 value -2.440343
iter  72 value -2.442094
iter  73 value -2.448355
iter  74 value -2.453493
iter  75 value -2.454521
iter  76 value -2.455149
iter  76 value -2.455149
iter  77 value -2.455631
iter  77 value -2.455631
iter  78 value -2.455665
iter  79 value -2.455668
iter  79 value -2.455668
iter  80 value -2.455670
iter  80 value -2.455670
iter  80 value -2.455670
final  value -2.455670 
converged
initial  value -2.365795 
iter   2 value -2.369653
iter   3 value -2.375767
iter   4 value -2.377556
iter   5 value -2.378507
iter   6 value -2.379245
iter   7 value -2.381124
iter   8 value -2.381922
iter   9 value -2.383133
iter  10 value -2.383789
iter  11 value -2.384564
iter  12 value -2.385885
iter  13 value -2.386312
iter  14 value -2.386556
iter  15 value -2.386631
iter  16 value -2.386651
iter  17 value -2.386673
iter  18 value -2.386679
iter  19 value -2.386688
iter  20 value -2.386697
iter  21 value -2.386711
iter  22 value -2.386734
iter  23 value -2.386766
iter  24 value -2.386816
iter  25 value -2.386820
iter  26 value -2.386826
iter  27 value -2.386839
iter  28 value -2.386846
iter  29 value -2.386852
iter  30 value -2.386862
iter  31 value -2.386865
iter  32 value -2.386867
iter  33 value -2.386870
iter  34 value -2.386872
iter  35 value -2.386875
iter  36 value -2.386886
iter  37 value -2.386898
iter  38 value -2.386907
iter  39 value -2.386918
iter  40 value -2.386921
iter  41 value -2.386926
iter  42 value -2.386928
iter  43 value -2.386929
iter  44 value -2.386930
iter  45 value -2.386931
iter  46 value -2.386932
iter  47 value -2.386932
iter  47 value -2.386932
final  value -2.386932 
converged

initial  value -2.201589 
iter   2 value -2.306262
iter   3 value -2.330457
iter   4 value -2.340046
iter   5 value -2.340298
iter   6 value -2.340422
iter   7 value -2.340524
iter   8 value -2.340525
iter   9 value -2.340525
iter   9 value -2.340525
iter   9 value -2.340525
final  value -2.340525 
converged
initial  value -2.350184 
iter   2 value -2.350215
iter   3 value -2.350222
iter   4 value -2.350228
iter   5 value -2.350229
iter   5 value -2.350229
iter   5 value -2.350229
final  value -2.350229 
converged

initial  value -2.201589 
iter   2 value -2.307314
iter   3 value -2.339021
iter   4 value -2.341656
iter   5 value -2.342933
iter   6 value -2.343701
iter   7 value -2.343907
iter   8 value -2.345854
iter   9 value -2.348079
iter  10 value -2.351043
iter  11 value -2.352641
iter  12 value -2.353296
iter  13 value -2.353309
iter  14 value -2.353320
iter  15 value -2.353320
iter  15 value -2.353320
iter  15 value -2.353320
final  value -2.353320 
converged
initial  value -2.359630 
iter   2 value -2.359689
iter   3 value -2.359833
iter   4 value -2.359971
iter   5 value -2.359988
iter   6 value -2.359989
iter   7 value -2.359991
iter   8 value -2.359992
iter   9 value -2.359993
iter   9 value -2.359993
iter   9 value -2.359993
final  value -2.359993 
converged

initial  value -2.201589 
iter   2 value -2.336670
iter   3 value -2.353593
iter   4 value -2.355752
iter   5 value -2.358016
iter   6 value -2.359331
iter   7 value -2.360610
iter   8 value -2.362526
iter   9 value -2.363002
iter  10 value -2.363074
iter  11 value -2.363260
iter  12 value -2.363738
iter  13 value -2.364351
iter  14 value -2.364859
iter  15 value -2.364944
iter  16 value -2.365055
iter  17 value -2.365064
iter  18 value -2.365098
iter  19 value -2.365123
iter  20 value -2.365131
iter  21 value -2.365146
iter  22 value -2.365152
iter  23 value -2.365163
iter  24 value -2.365164
iter  25 value -2.365165
iter  26 value -2.365165
iter  27 value -2.365166
iter  28 value -2.365167
iter  29 value -2.365168
iter  29 value -2.365168
iter  29 value -2.365168
final  value -2.365168 
converged
initial  value -2.372411 
iter   2 value -2.372440
iter   3 value -2.372445
iter   4 value -2.372582
iter   5 value -2.372598
iter   6 value -2.372623
iter   7 value -2.372642
iter   8 value -2.372646
iter   9 value -2.372646
iter  10 value -2.372647
iter  11 value -2.372648
iter  12 value -2.372651
iter  13 value -2.372655
iter  14 value -2.372659
iter  15 value -2.372661
iter  16 value -2.372661
iter  16 value -2.372661
final  value -2.372661 
converged

initial  value -2.201589 
iter   2 value -2.351048
iter   3 value -2.358347
iter   4 value -2.359025
iter   5 value -2.360318
iter   6 value -2.360935
iter   7 value -2.361388
iter   8 value -2.361595
iter   9 value -2.361738
iter  10 value -2.361895
iter  11 value -2.361951
iter  12 value -2.362009
iter  13 value -2.362190
iter  14 value -2.362347
iter  15 value -2.362450
iter  16 value -2.362483
iter  17 value -2.362523
iter  18 value -2.362635
iter  19 value -2.362702
iter  20 value -2.362730
iter  21 value -2.362792
iter  22 value -2.362904
iter  23 value -2.363248
iter  24 value -2.364650
iter  25 value -2.364791
iter  26 value -2.365015
iter  27 value -2.366326
iter  28 value -2.367234
iter  29 value -2.368086
iter  30 value -2.368528
iter  31 value -2.368774
iter  32 value -2.369083
iter  33 value -2.369183
iter  34 value -2.369290
iter  35 value -2.369422
iter  36 value -2.369432
iter  37 value -2.369449
iter  38 value -2.369459
iter  39 value -2.369459
iter  40 value -2.369475
iter  41 value -2.369531
iter  42 value -2.369536
iter  43 value -2.369544
iter  44 value -2.369556
iter  45 value -2.369559
iter  46 value -2.369562
iter  47 value -2.369565
iter  48 value -2.369568
iter  49 value -2.369569
iter  50 value -2.369569
iter  50 value -2.369569
iter  50 value -2.369569
final  value -2.369569 
converged
initial  value -2.373512 
iter   2 value -2.373526
iter   3 value -2.373659
iter   4 value -2.373698
iter   5 value -2.373751
iter   6 value -2.373786
iter   7 value -2.373804
iter   8 value -2.373840
iter   9 value -2.373864
iter  10 value -2.373882
iter  11 value -2.373909
iter  12 value -2.373919
iter  13 value -2.373923
iter  14 value -2.373926
iter  15 value -2.373932
iter  16 value -2.373942
iter  17 value -2.373960
iter  18 value -2.374047
iter  19 value -2.374055
iter  20 value -2.374067
iter  21 value -2.374074
iter  22 value -2.374083
iter  23 value -2.374102
iter  24 value -2.374177
iter  25 value -2.376110
iter  26 value -2.376576
iter  27 value -2.376660
iter  28 value -2.377297
iter  29 value -2.377758
iter  30 value -2.377968
iter  31 value -2.378334
iter  32 value -2.380625
iter  33 value -2.383082
iter  34 value -2.383801
iter  35 value -2.387257
iter  36 value -2.387946
iter  37 value -2.388106
iter  38 value -2.388215
iter  39 value -2.388264
iter  40 value -2.388314
iter  41 value -2.388325
iter  42 value -2.388326
iter  42 value -2.388326
final  value -2.388326 
converged

initial  value -2.201589 
iter   2 value -2.300325
iter   3 value -2.324784
iter   4 value -2.353709
iter   5 value -2.357230
iter   6 value -2.360813
iter   7 value -2.361798
iter   8 value -2.361955
iter   9 value -2.362052
iter  10 value -2.362157
iter  11 value -2.362238
iter  12 value -2.362294
iter  13 value -2.362370
iter  14 value -2.362613
iter  15 value -2.362709
iter  16 value -2.362795
iter  17 value -2.362891
iter  18 value -2.363140
iter  19 value -2.364101
iter  20 value -2.364402
iter  21 value -2.364615
iter  22 value -2.364791
iter  23 value -2.364979
iter  24 value -2.365411
iter  25 value -2.366594
iter  26 value -2.367048
iter  27 value -2.367773
iter  28 value -2.368304
iter  29 value -2.368443
iter  30 value -2.368695
iter  31 value -2.368750
iter  32 value -2.368876
iter  33 value -2.369213
iter  34 value -2.369903
iter  35 value -2.370752
iter  36 value -2.371708
iter  37 value -2.373006
iter  38 value -2.373377
iter  39 value -2.376087
iter  40 value -2.379424
iter  41 value -2.381030
iter  42 value -2.383583
iter  43 value -2.385003
iter  44 value -2.389110
iter  45 value -2.392012
iter  46 value -2.392909
iter  47 value -2.393573
iter  48 value -2.395631
iter  49 value -2.398267
iter  50 value -2.399388
iter  51 value -2.402735
iter  52 value -2.404070
iter  53 value -2.406005
iter  54 value -2.407600
iter  55 value -2.409158
iter  56 value -2.410021
iter  57 value -2.410401
iter  58 value -2.412132
iter  59 value -2.414228
iter  60 value -2.416946
iter  61 value -2.419010
iter  62 value -2.421673
iter  63 value -2.421942
iter  64 value -2.422703
iter  65 value -2.425364
iter  66 value -2.427272
iter  67 value -2.429110
iter  68 value -2.430674
iter  69 value -2.432869
iter  70 value -2.436232
iter  71 value -2.438258
iter  72 value -2.441984
iter  73 value -2.444752
iter  74 value -2.447297
iter  75 value -2.447370
iter  76 value -2.450260
iter  77 value -2.450293
iter  78 value -2.455062
iter  79 value -2.456695
iter  80 value -2.457089
iter  81 value -2.458237
iter  82 value -2.461254
iter  83 value -2.462968
iter  84 value -2.464884
iter  85 value -2.464996
iter  86 value -2.465069
iter  87 value -2.465074
iter  87 value -2.465074
iter  88 value -2.466144
iter  89 value -2.466203
iter  90 value -2.467712
iter  90 value -2.467712
iter  91 value -2.471544
iter  92 value -2.471765
iter  93 value -2.472446
iter  94 value -2.472455
iter  95 value -2.474107
iter  96 value -2.474200
iter  97 value -2.474854
iter  98 value -2.474884
iter  99 value -2.475777
iter 100 value -2.475824
final  value -2.475824 
stopped after 100 iterations
initial  value -2.213853 
iter   2 value -2.306718
iter   3 value -2.331530
iter   4 value -2.361788
iter   5 value -2.364711
iter   6 value -2.366412
iter   7 value -2.367335
iter   8 value -2.367897
iter   9 value -2.368347
iter  10 value -2.368376
iter  11 value -2.368472
iter  12 value -2.368679
iter  13 value -2.368987
iter  14 value -2.369039
iter  15 value -2.369698
iter  16 value -2.370337
iter  17 value -2.370405
iter  18 value -2.370878
iter  19 value -2.371545
iter  20 value -2.371790
iter  21 value -2.372616
iter  22 value -2.372947
iter  23 value -2.373193
iter  24 value -2.373376
iter  25 value -2.373728
iter  26 value -2.376191
iter  27 value -2.377511
iter  28 value -2.379467
iter  29 value -2.381458
iter  30 value -2.382809
iter  31 value -2.383575
iter  32 value -2.383947
iter  33 value -2.384086
iter  34 value -2.384704
iter  35 value -2.384809
iter  36 value -2.384857
iter  37 value -2.384881
iter  38 value -2.384906
iter  39 value -2.384972
iter  40 value -2.385079
iter  41 value -2.385189
iter  42 value -2.385781
iter  43 value -2.386339
iter  44 value -2.386410
iter  45 value -2.386500
iter  46 value -2.386818
iter  47 value -2.387047
iter  48 value -2.387251
iter  49 value -2.387494
iter  50 value -2.387699
iter  51 value -2.388211
iter  52 value -2.388874
iter  53 value -2.389984
iter  54 value -2.391497
iter  55 value -2.391946
iter  56 value -2.392542
iter  57 value -2.393146
iter  58 value -2.394068
iter  59 value -2.395034
iter  60 value -2.395851
iter  61 value -2.396642
iter  62 value -2.397457
iter  63 value -2.397599
iter  64 value -2.397844
iter  65 value -2.397984
iter  66 value -2.398652
iter  67 value -2.398818
iter  68 value -2.399311
iter  69 value -2.399673
iter  70 value -2.399860
iter  71 value -2.400051
iter  72 value -2.400181
iter  73 value -2.400293
iter  74 value -2.400401
iter  75 value -2.400470
iter  76 value -2.400537
iter  77 value -2.400590
iter  78 value -2.400632
iter  79 value -2.400688
iter  80 value -2.400732
iter  81 value -2.400806
iter  82 value -2.400809
iter  83 value -2.400814
iter  84 value -2.400854
iter  85 value -2.401037
iter  86 value -2.401129
iter  87 value -2.401233
iter  88 value -2.401311
iter  89 value -2.401495
iter  90 value -2.401530
iter  91 value -2.401616
iter  92 value -2.401694
iter  93 value -2.401839
iter  94 value -2.401884
iter  95 value -2.401913
iter  96 value -2.401988
iter  97 value -2.402030
iter  98 value -2.402079
iter  99 value -2.402153
iter 100 value -2.402394
final  value -2.402394 
stopped after 100 iterations

initial  value -2.201589 
iter   2 value -2.295774
iter   3 value -2.318818
iter   4 value -2.330222
iter   5 value -2.354124
iter   6 value -2.358694
iter   7 value -2.360649
iter   8 value -2.361080
iter   9 value -2.361255
iter  10 value -2.361652
iter  11 value -2.364150
iter  12 value -2.365476
iter  13 value -2.366416
iter  14 value -2.367217
iter  15 value -2.368083
iter  16 value -2.368223
iter  17 value -2.368310
iter  18 value -2.368657
iter  19 value -2.368865
iter  20 value -2.369354
iter  21 value -2.370220
iter  22 value -2.371950
iter  23 value -2.372459
iter  24 value -2.372811
iter  25 value -2.373517
iter  26 value -2.373973
iter  27 value -2.374553
iter  28 value -2.376296
iter  29 value -2.377843
iter  30 value -2.378960
iter  31 value -2.380923
iter  32 value -2.381764
iter  33 value -2.383905
iter  34 value -2.384749
iter  35 value -2.389261
iter  36 value -2.394683
iter  37 value -2.400369
iter  38 value -2.402257
iter  39 value -2.403523
iter  40 value -2.407055
iter  41 value -2.411747
iter  42 value -2.416810
iter  43 value -2.423608
iter  44 value -2.426539
iter  45 value -2.427700
iter  46 value -2.433149
iter  47 value -2.435760
iter  48 value -2.442731
iter  49 value -2.447176
iter  50 value -2.454713
iter  51 value -2.456641
iter  52 value -2.457665
iter  53 value -2.466185
iter  54 value -2.469400
iter  55 value -2.474698
iter  56 value -2.478989
iter  57 value -2.482519
iter  58 value -2.482882
iter  58 value -2.482882
iter  59 value -2.486026
iter  60 value -2.486165
iter  61 value -2.488555
iter  62 value -2.491044
iter  63 value -2.491119
iter  64 value -2.491518
iter  65 value -2.491682
iter  66 value -2.491686
iter  67 value -2.492006
iter  68 value -2.492175
iter  69 value -2.492179
iter  70 value -2.492480
iter  71 value -2.492658
iter  72 value -2.492662
iter  73 value -2.492941
iter  74 value -2.493149
iter  75 value -2.493150
iter  76 value -2.493167
iter  77 value -2.493842
iter  78 value -2.493864
iter  79 value -2.494160
iter  80 value -2.494180
iter  81 value -2.494181
iter  82 value -2.494272
iter  83 value -2.494277
iter  84 value -2.494353
iter  85 value -2.494354
iter  86 value -2.494488
iter  87 value -2.494517
iter  88 value -2.494673
iter  89 value -2.494675
iter  90 value -2.494826
iter  91 value -2.495065
iter  92 value -2.495068
iter  93 value -2.495347
iter  94 value -2.495443
iter  95 value -2.495445
iter  96 value -2.495568
iter  97 value -2.495722
iter  98 value -2.495724
iter  99 value -2.495940
iter 100 value -2.496029
final  value -2.496029 
stopped after 100 iterations
initial  value -2.213853 
iter   2 value -2.301593
iter   3 value -2.323716
iter   4 value -2.330368
iter   5 value -2.340249
iter   6 value -2.355477
iter   7 value -2.363811
iter   8 value -2.364444
iter   9 value -2.367009
iter  10 value -2.367717
iter  11 value -2.368173
iter  12 value -2.368352
iter  13 value -2.369162
iter  14 value -2.369220
iter  15 value -2.372557
iter  16 value -2.375801
iter  17 value -2.377171
iter  18 value -2.378502
iter  19 value -2.379518
iter  20 value -2.379847
iter  21 value -2.380202
iter  22 value -2.380949
iter  23 value -2.380987
iter  24 value -2.381257
iter  25 value -2.381316
iter  26 value -2.382557
iter  27 value -2.382972
iter  28 value -2.383351
iter  29 value -2.383805
iter  30 value -2.384365
iter  31 value -2.384784
iter  32 value -2.385137
iter  33 value -2.385255
iter  34 value -2.385302
iter  35 value -2.385361
iter  36 value -2.385407
iter  37 value -2.385462
iter  38 value -2.385558
iter  39 value -2.385669
iter  40 value -2.385749
iter  41 value -2.385848
iter  42 value -2.385857
iter  43 value -2.385860
iter  44 value -2.385861
iter  45 value -2.385861
iter  46 value -2.385861
iter  46 value -2.385861
iter  46 value -2.385861
final  value -2.385861 
converged

initial  value -2.201589 
iter   2 value -2.295805
iter   3 value -2.319154
iter   4 value -2.333569
iter   5 value -2.356875
iter   6 value -2.359961
iter   7 value -2.361391
iter   8 value -2.361865
iter   9 value -2.362189
iter  10 value -2.363278
iter  11 value -2.367052
iter  12 value -2.370832
iter  13 value -2.377951
iter  14 value -2.381764
iter  15 value -2.384653
iter  16 value -2.386194
iter  17 value -2.389441
iter  18 value -2.391769
iter  19 value -2.397060
iter  20 value -2.397564
iter  21 value -2.403657
iter  22 value -2.407625
iter  23 value -2.410574
iter  24 value -2.421143
iter  25 value -2.422775
iter  26 value -2.424889
iter  27 value -2.427350
iter  28 value -2.431377
iter  29 value -2.448913
iter  30 value -2.450433
iter  31 value -2.452992
iter  32 value -2.458434
iter  33 value -2.465071
iter  34 value -2.469280
iter  35 value -2.472841
iter  36 value -2.473578
iter  37 value -2.476349
iter  38 value -2.482030
iter  39 value -2.490448
iter  40 value -2.493889
iter  41 value -2.500129
iter  42 value -2.501514
iter  43 value -2.504087
iter  44 value -2.506708
iter  45 value -2.507869
iter  46 value -2.509256
iter  47 value -2.510588
iter  48 value -2.511521
iter  49 value -2.511724
iter  50 value -2.511753
iter  51 value -2.517238
iter  52 value -2.517808
iter  53 value -2.518962
iter  54 value -2.520424
iter  55 value -2.520729
iter  56 value -2.521009
iter  57 value -2.521765
iter  58 value -2.523078
iter  59 value -2.523364
iter  60 value -2.523908
iter  61 value -2.524052
iter  62 value -2.524118
iter  63 value -2.524511
iter  64 value -2.524564
iter  65 value -2.525527
iter  66 value -2.525527
iter  67 value -2.526751
iter  68 value -2.526966
iter  69 value -2.527277
iter  70 value -2.528357
iter  71 value -2.530646
iter  72 value -2.531146
iter  73 value -2.531450
iter  74 value -2.531591
iter  75 value -2.531933
iter  76 value -2.531997
iter  77 value -2.532090
iter  78 value -2.532093
iter  79 value -2.532105
iter  80 value -2.532119
iter  81 value -2.532560
iter  82 value -2.532999
iter  83 value -2.533003
iter  84 value -2.533003
iter  85 value -2.533036
iter  86 value -2.533429
iter  87 value -2.534572
iter  88 value -2.534574
iter  89 value -2.534582
iter  90 value -2.534593
iter  91 value -2.534606
iter  92 value -2.534993
iter  93 value -2.534994
iter  94 value -2.535029
iter  95 value -2.535043
iter  96 value -2.535058
iter  97 value -2.535380
iter  98 value -2.535385
iter  99 value -2.535387
iter 100 value -2.535507
final  value -2.535507 
stopped after 100 iterations
initial  value -2.213853 
iter   2 value -2.301970
iter   3 value -2.324306
iter   4 value -2.334974
iter   5 value -2.349239
iter   6 value -2.360977
iter   7 value -2.365867
iter   8 value -2.367935
iter   9 value -2.368872
iter  10 value -2.369285
iter  11 value -2.369673
iter  12 value -2.371868
iter  13 value -2.374828
iter  14 value -2.379420
iter  15 value -2.381265
iter  16 value -2.385643
iter  17 value -2.391349
iter  18 value -2.396277
iter  19 value -2.397384
iter  20 value -2.397466
iter  21 value -2.399351
iter  22 value -2.399670
iter  23 value -2.401130
iter  24 value -2.402147
iter  25 value -2.403488
iter  26 value -2.403825
iter  27 value -2.403911
iter  28 value -2.404074
iter  29 value -2.404323
iter  30 value -2.404677
iter  31 value -2.404882
iter  32 value -2.405503
iter  33 value -2.405850
iter  34 value -2.406064
iter  35 value -2.406184
iter  36 value -2.406293
iter  37 value -2.406453
iter  38 value -2.406646
iter  39 value -2.406802
iter  40 value -2.406874
iter  41 value -2.407372
iter  42 value -2.407628
iter  43 value -2.407829
iter  44 value -2.407862
iter  45 value -2.407868
iter  46 value -2.407870
iter  47 value -2.407870
iter  47 value -2.407870
final  value -2.407870 
converged

initial  value -2.201589 
iter   2 value -2.297865
iter   3 value -2.321098
iter   4 value -2.342587
iter   5 value -2.354283
iter   6 value -2.360356
iter   7 value -2.362454
iter   8 value -2.362839
iter   9 value -2.363059
iter  10 value -2.363875
iter  11 value -2.366126
iter  12 value -2.368134
iter  13 value -2.369135
iter  14 value -2.374886
iter  15 value -2.381101
iter  16 value -2.384829
iter  17 value -2.386524
iter  18 value -2.388077
iter  19 value -2.392603
iter  20 value -2.395252
iter  21 value -2.396080
iter  22 value -2.398440
iter  23 value -2.402307
iter  24 value -2.413694
iter  25 value -2.422124
iter  26 value -2.428926
iter  27 value -2.430225
iter  28 value -2.432092
iter  29 value -2.434415
iter  30 value -2.440876
iter  31 value -2.444742
iter  32 value -2.446579
iter  33 value -2.455991
iter  34 value -2.458154
iter  35 value -2.465577
iter  36 value -2.468457
iter  37 value -2.472203
iter  38 value -2.472834
iter  39 value -2.480854
iter  40 value -2.481958
iter  40 value -2.481958
iter  41 value -2.487759
iter  42 value -2.487871
iter  43 value -2.489345
iter  44 value -2.489365
iter  45 value -2.490045
iter  46 value -2.491200
iter  46 value -2.491200
iter  47 value -2.493826
iter  48 value -2.494277
iter  49 value -2.494493
iter  50 value -2.494500
iter  51 value -2.494536
iter  52 value -2.494541
iter  53 value -2.494541
iter  54 value -2.494569
iter  55 value -2.494611
iter  56 value -2.494625
iter  57 value -2.494670
iter  58 value -2.494715
iter  59 value -2.494736
iter  60 value -2.494758
iter  61 value -2.494798
iter  62 value -2.494809
iter  63 value -2.494823
iter  64 value -2.494860
iter  65 value -2.494867
iter  66 value -2.494881
iter  67 value -2.494917
iter  68 value -2.494925
iter  69 value -2.494940
iter  70 value -2.494976
iter  71 value -2.494986
iter  72 value -2.495005
iter  73 value -2.495042
iter  74 value -2.495047
iter  75 value -2.495101
iter  76 value -2.495148
iter  77 value -2.495177
iter  78 value -2.495213
iter  78 value -2.495213
iter  79 value -2.495299
iter  80 value -2.495332
iter  81 value -2.495461
iter  82 value -2.495542
iter  83 value -2.495637
iter  84 value -2.495693
iter  85 value -2.495797
iter  86 value -2.495871
iter  87 value -2.495960
iter  88 value -2.496025
iter  89 value -2.496113
iter  90 value -2.496186
iter  91 value -2.496266
iter  92 value -2.496335
iter  93 value -2.496412
iter  94 value -2.496486
iter  95 value -2.496556
iter  96 value -2.496629
iter  97 value -2.496695
iter  98 value -2.496770
iter  99 value -2.496832
iter 100 value -2.496906
final  value -2.496906 
stopped after 100 iterations
initial  value -2.213853 
iter   2 value -2.304045
iter   3 value -2.326049
iter   4 value -2.344123
iter   5 value -2.354738
iter   6 value -2.366235
iter   7 value -2.367790
iter   8 value -2.369276
iter   9 value -2.369686
iter  10 value -2.370099
iter  11 value -2.370482
iter  12 value -2.372843
iter  13 value -2.376396
iter  14 value -2.377385
iter  15 value -2.378485
iter  16 value -2.380879
iter  17 value -2.383534
iter  18 value -2.386513
iter  19 value -2.387203
iter  20 value -2.391164
iter  21 value -2.391579
iter  22 value -2.393076
iter  23 value -2.395467
iter  24 value -2.395653
iter  25 value -2.397000
iter  26 value -2.397930
iter  27 value -2.398057
iter  28 value -2.398562
iter  29 value -2.399778
iter  30 value -2.399791
iter  31 value -2.399942
iter  32 value -2.400864
iter  33 value -2.401343
iter  34 value -2.403685
iter  35 value -2.404471
iter  36 value -2.405321
iter  37 value -2.406193
iter  38 value -2.406283
iter  39 value -2.406350
iter  40 value -2.406428
iter  41 value -2.406445
iter  42 value -2.406468
iter  43 value -2.406499
iter  44 value -2.406535
iter  45 value -2.406627
iter  46 value -2.406702
iter  47 value -2.406812
iter  48 value -2.407095
iter  49 value -2.407110
iter  50 value -2.407303
iter  51 value -2.407352
iter  52 value -2.407354
iter  53 value -2.407357
iter  54 value -2.407363
iter  55 value -2.407390
iter  56 value -2.407399
iter  57 value -2.407481
iter  58 value -2.407543
iter  59 value -2.407590
iter  60 value -2.407663
iter  61 value -2.407697
iter  62 value -2.407731
iter  63 value -2.407755
iter  64 value -2.407784
iter  65 value -2.407830
iter  66 value -2.407897
iter  67 value -2.407919
iter  68 value -2.407977
iter  69 value -2.407992
iter  70 value -2.407998
iter  71 value -2.407999
iter  72 value -2.407999
iter  73 value -2.407999
iter  74 value -2.407999
iter  75 value -2.408000
iter  75 value -2.408000
iter  75 value -2.408000
final  value -2.408000 
converged

initial  value -2.197587 
iter   2 value -2.302454
iter   3 value -2.338428
iter   4 value -2.355919
iter   5 value -2.356806
iter   6 value -2.357706
iter   7 value -2.358177
iter   8 value -2.358216
iter   9 value -2.358216
iter   9 value -2.358216
iter   9 value -2.358216
final  value -2.358216 
converged
initial  value -2.369568 
iter   2 value -2.369639
iter   3 value -2.369649
iter   4 value -2.369685
iter   5 value -2.369688
iter   6 value -2.369688
iter   6 value -2.369688
iter   6 value -2.369688
final  value -2.369688 
converged

initial  value -2.197587 
iter   2 value -2.309411
iter   3 value -2.354263
iter   4 value -2.356137
iter   5 value -2.360460
iter   6 value -2.362968
iter   7 value -2.363379
iter   8 value -2.363407
iter   9 value -2.363449
iter  10 value -2.363629
iter  11 value -2.363768
iter  12 value -2.363829
iter  13 value -2.363835
iter  14 value -2.363835
iter  14 value -2.363835
iter  14 value -2.363835
final  value -2.363835 
converged
initial  value -2.374296 
iter   2 value -2.374380
iter   3 value -2.374434
iter   4 value -2.374473
iter   5 value -2.374480
iter   6 value -2.374481
iter   7 value -2.374490
iter   8 value -2.374493
iter   9 value -2.374494
iter   9 value -2.374494
iter   9 value -2.374494
final  value -2.374494 
converged

initial  value -2.197587 
iter   2 value -2.338157
iter   3 value -2.357278
iter   4 value -2.359925
iter   5 value -2.362472
iter   6 value -2.362689
iter   7 value -2.362982
iter   8 value -2.362993
iter   9 value -2.363039
iter  10 value -2.363141
iter  11 value -2.363268
iter  12 value -2.363361
iter  13 value -2.363400
iter  14 value -2.363436
iter  15 value -2.363508
iter  16 value -2.363641
iter  17 value -2.363779
iter  18 value -2.363857
iter  19 value -2.363862
iter  20 value -2.363864
iter  21 value -2.363870
iter  22 value -2.363871
iter  23 value -2.363871
iter  24 value -2.363871
iter  25 value -2.363871
iter  26 value -2.363871
iter  26 value -2.363871
iter  26 value -2.363871
final  value -2.363871 
converged
initial  value -2.374427 
iter   2 value -2.374529
iter   3 value -2.374577
iter   4 value -2.374613
iter   5 value -2.374619
iter   6 value -2.374628
iter   7 value -2.374648
iter   8 value -2.374655
iter   9 value -2.374656
iter  10 value -2.374656
iter  11 value -2.374657
iter  12 value -2.374660
iter  13 value -2.374662
iter  14 value -2.374664
iter  15 value -2.374664
iter  15 value -2.374664
iter  15 value -2.374664
final  value -2.374664 
converged

initial  value -2.197587 
iter   2 value -2.347513
iter   3 value -2.359831
iter   4 value -2.360586
iter   5 value -2.361581
iter   6 value -2.362065
iter   7 value -2.362196
iter   8 value -2.362437
iter   9 value -2.362859
iter  10 value -2.363110
iter  11 value -2.363185
iter  12 value -2.363208
iter  13 value -2.363239
iter  14 value -2.363323
iter  15 value -2.363542
iter  16 value -2.363703
iter  17 value -2.363847
iter  18 value -2.363870
iter  19 value -2.363870
iter  19 value -2.363870
iter  19 value -2.363870
final  value -2.363870 
converged
initial  value -2.374441 
iter   2 value -2.374544
iter   3 value -2.374592
iter   4 value -2.374630
iter   5 value -2.374638
iter   6 value -2.374650
iter   7 value -2.374662
iter   8 value -2.374668
iter   9 value -2.374673
iter  10 value -2.374684
iter  11 value -2.374708
iter  12 value -2.374817
iter  13 value -2.374872
iter  14 value -2.374958
iter  15 value -2.375094
iter  16 value -2.375232
iter  17 value -2.375514
iter  18 value -2.375936
iter  19 value -2.376464
iter  20 value -2.377256
iter  21 value -2.378202
iter  22 value -2.378793
iter  23 value -2.379069
iter  24 value -2.380137
iter  25 value -2.381259
iter  26 value -2.382514
iter  27 value -2.383434
iter  28 value -2.383803
iter  29 value -2.385385
iter  30 value -2.387080
iter  31 value -2.390886
iter  32 value -2.391612
iter  33 value -2.392840
iter  34 value -2.393573
iter  35 value -2.393779
iter  36 value -2.394193
iter  37 value -2.394268
iter  38 value -2.394339
iter  39 value -2.394471
iter  40 value -2.394484
iter  41 value -2.394506
iter  42 value -2.394525
iter  43 value -2.394564
iter  44 value -2.394573
iter  45 value -2.394761
iter  46 value -2.394781
iter  47 value -2.394902
iter  48 value -2.394968
iter  49 value -2.395134
iter  50 value -2.395351
iter  51 value -2.395515
iter  52 value -2.395676
iter  53 value -2.396003
iter  54 value -2.396318
iter  55 value -2.397235
iter  56 value -2.397348
iter  57 value -2.397605
iter  58 value -2.397617
iter  59 value -2.397618
iter  60 value -2.397619
iter  61 value -2.397628
iter  62 value -2.397629
iter  63 value -2.397630
iter  64 value -2.397631
iter  65 value -2.397631
iter  66 value -2.397632
iter  67 value -2.397632
iter  68 value -2.397632
iter  68 value -2.397632
iter  68 value -2.397632
final  value -2.397632 
converged

initial  value -2.197587 
iter   2 value -2.302879
iter   3 value -2.324965
iter   4 value -2.348279
iter   5 value -2.348795
iter   6 value -2.357194
iter   7 value -2.361086
iter   8 value -2.361731
iter   9 value -2.361880
iter  10 value -2.362011
iter  11 value -2.363296
iter  12 value -2.363751
iter  13 value -2.363908
iter  14 value -2.363946
iter  15 value -2.363949
iter  16 value -2.363951
iter  17 value -2.363957
iter  18 value -2.363964
iter  19 value -2.363976
iter  20 value -2.364006
iter  21 value -2.364061
iter  22 value -2.364131
iter  23 value -2.364193
iter  24 value -2.364226
iter  25 value -2.364336
iter  26 value -2.364351
iter  27 value -2.364356
iter  28 value -2.364363
iter  29 value -2.364408
iter  30 value -2.364473
iter  31 value -2.364515
iter  32 value -2.364545
iter  33 value -2.364548
iter  34 value -2.364552
iter  35 value -2.364645
iter  36 value -2.364793
iter  37 value -2.364920
iter  38 value -2.364937
iter  39 value -2.364955
iter  40 value -2.364982
iter  41 value -2.365012
iter  42 value -2.365120
iter  43 value -2.365778
iter  44 value -2.366082
iter  45 value -2.366143
iter  46 value -2.366288
iter  47 value -2.366646
iter  48 value -2.367185
iter  49 value -2.368101
iter  50 value -2.369177
iter  51 value -2.370330
iter  52 value -2.371890
iter  53 value -2.374308
iter  54 value -2.379151
iter  55 value -2.380379
iter  56 value -2.381915
iter  57 value -2.382667
iter  58 value -2.383884
iter  59 value -2.384909
iter  60 value -2.387374
iter  61 value -2.390230
iter  62 value -2.392300
iter  63 value -2.394034
iter  64 value -2.398372
iter  65 value -2.406659
iter  66 value -2.411356
iter  67 value -2.411760
iter  68 value -2.412086
iter  69 value -2.412343
iter  70 value -2.413143
iter  71 value -2.413559
iter  72 value -2.414062
iter  73 value -2.414225
iter  74 value -2.414647
iter  75 value -2.415294
iter  76 value -2.416012
iter  77 value -2.416557
iter  78 value -2.416659
iter  79 value -2.416681
iter  80 value -2.416698
iter  81 value -2.416712
iter  82 value -2.416731
iter  83 value -2.416741
iter  84 value -2.416747
iter  85 value -2.416748
iter  86 value -2.416748
iter  87 value -2.416749
iter  88 value -2.416749
iter  89 value -2.416749
iter  89 value -2.416749
iter  89 value -2.416749
final  value -2.416749 
converged

Error in stats::arima(xdata, order = c(p, d, q), seasonal = list(order = c(P,  : 
  non-stationary AR part from CSS

p_best=which.min( apply(aic,1,min) ) -1 
q_best=which.min( apply(aic,2,min) ) -1 
p_best

[1] 4

q_best

[1] 4

b = auto.arima(gtemp)
fit=sarima(gtemp,p_best,1,q_best)

initial  value -2.201589 
iter   2 value -2.300325
iter   3 value -2.324784
iter   4 value -2.353709
iter   5 value -2.357230
iter   6 value -2.360813
iter   7 value -2.361798
iter   8 value -2.361955
iter   9 value -2.362052
iter  10 value -2.362157
iter  11 value -2.362238
iter  12 value -2.362294
iter  13 value -2.362370
iter  14 value -2.362613
iter  15 value -2.362709
iter  16 value -2.362795
iter  17 value -2.362891
iter  18 value -2.363140
iter  19 value -2.364101
iter  20 value -2.364402
iter  21 value -2.364615
iter  22 value -2.364791
iter  23 value -2.364979
iter  24 value -2.365411
iter  25 value -2.366594
iter  26 value -2.367048
iter  27 value -2.367773
iter  28 value -2.368304
iter  29 value -2.368443
iter  30 value -2.368695
iter  31 value -2.368750
iter  32 value -2.368876
iter  33 value -2.369213
iter  34 value -2.369903
iter  35 value -2.370752
iter  36 value -2.371708
iter  37 value -2.373006
iter  38 value -2.373377
iter  39 value -2.376087
iter  40 value -2.379424
iter  41 value -2.381030
iter  42 value -2.383583
iter  43 value -2.385003
iter  44 value -2.389110
iter  45 value -2.392012
iter  46 value -2.392909
iter  47 value -2.393573
iter  48 value -2.395631
iter  49 value -2.398267
iter  50 value -2.399388
iter  51 value -2.402735
iter  52 value -2.404070
iter  53 value -2.406005
iter  54 value -2.407600
iter  55 value -2.409158
iter  56 value -2.410021
iter  57 value -2.410401
iter  58 value -2.412132
iter  59 value -2.414228
iter  60 value -2.416946
iter  61 value -2.419010
iter  62 value -2.421673
iter  63 value -2.421942
iter  64 value -2.422703
iter  65 value -2.425364
iter  66 value -2.427272
iter  67 value -2.429110
iter  68 value -2.430674
iter  69 value -2.432869
iter  70 value -2.436232
iter  71 value -2.438258
iter  72 value -2.441984
iter  73 value -2.444752
iter  74 value -2.447297
iter  75 value -2.447370
iter  76 value -2.450260
iter  77 value -2.450293
iter  78 value -2.455062
iter  79 value -2.456695
iter  80 value -2.457089
iter  81 value -2.458237
iter  82 value -2.461254
iter  83 value -2.462968
iter  84 value -2.464884
iter  85 value -2.464996
iter  86 value -2.465069
iter  87 value -2.465074
iter  87 value -2.465074
iter  88 value -2.466144
iter  89 value -2.466203
iter  90 value -2.467712
iter  90 value -2.467712
iter  91 value -2.471544
iter  92 value -2.471765
iter  93 value -2.472446
iter  94 value -2.472455
iter  95 value -2.474107
iter  96 value -2.474200
iter  97 value -2.474854
iter  98 value -2.474884
iter  99 value -2.475777
iter 100 value -2.475824
final  value -2.475824 
stopped after 100 iterations
initial  value -2.213853 
iter   2 value -2.306718
iter   3 value -2.331530
iter   4 value -2.361788
iter   5 value -2.364711
iter   6 value -2.366412
iter   7 value -2.367335
iter   8 value -2.367897
iter   9 value -2.368347
iter  10 value -2.368376
iter  11 value -2.368472
iter  12 value -2.368679
iter  13 value -2.368987
iter  14 value -2.369039
iter  15 value -2.369698
iter  16 value -2.370337
iter  17 value -2.370405
iter  18 value -2.370878
iter  19 value -2.371545
iter  20 value -2.371790
iter  21 value -2.372616
iter  22 value -2.372947
iter  23 value -2.373193
iter  24 value -2.373376
iter  25 value -2.373728
iter  26 value -2.376191
iter  27 value -2.377511
iter  28 value -2.379467
iter  29 value -2.381458
iter  30 value -2.382809
iter  31 value -2.383575
iter  32 value -2.383947
iter  33 value -2.384086
iter  34 value -2.384704
iter  35 value -2.384809
iter  36 value -2.384857
iter  37 value -2.384881
iter  38 value -2.384906
iter  39 value -2.384972
iter  40 value -2.385079
iter  41 value -2.385189
iter  42 value -2.385781
iter  43 value -2.386339
iter  44 value -2.386410
iter  45 value -2.386500
iter  46 value -2.386818
iter  47 value -2.387047
iter  48 value -2.387251
iter  49 value -2.387494
iter  50 value -2.387699
iter  51 value -2.388211
iter  52 value -2.388874
iter  53 value -2.389984
iter  54 value -2.391497
iter  55 value -2.391946
iter  56 value -2.392542
iter  57 value -2.393146
iter  58 value -2.394068
iter  59 value -2.395034
iter  60 value -2.395851
iter  61 value -2.396642
iter  62 value -2.397457
iter  63 value -2.397599
iter  64 value -2.397844
iter  65 value -2.397984
iter  66 value -2.398652
iter  67 value -2.398818
iter  68 value -2.399311
iter  69 value -2.399673
iter  70 value -2.399860
iter  71 value -2.400051
iter  72 value -2.400181
iter  73 value -2.400293
iter  74 value -2.400401
iter  75 value -2.400470
iter  76 value -2.400537
iter  77 value -2.400590
iter  78 value -2.400632
iter  79 value -2.400688
iter  80 value -2.400732
iter  81 value -2.400806
iter  82 value -2.400809
iter  83 value -2.400814
iter  84 value -2.400854
iter  85 value -2.401037
iter  86 value -2.401129
iter  87 value -2.401233
iter  88 value -2.401311
iter  89 value -2.401495
iter  90 value -2.401530
iter  91 value -2.401616
iter  92 value -2.401694
iter  93 value -2.401839
iter  94 value -2.401884
iter  95 value -2.401913
iter  96 value -2.401988
iter  97 value -2.402030
iter  98 value -2.402079
iter  99 value -2.402153
iter 100 value -2.402394
final  value -2.402394 
stopped after 100 iterations

possible convergence problem: optim gave code = 1

fore = sarima.for(gtemp, n.ahead=10, p_best, 1, q_best)

possible convergence problem: optim gave code = 1

plot( window(gtemp, start=1980, end=2009), type='o', pch=16,
      lwd=2, xlim=c(1980,2020), ylim=c(0,.9), ylab='gtemp')
lines(2010:2019,fore$pred, type='o', pch=16, col=2)

lines(2010:2019,fore$pred + 1.96*fore$se, lty=2, lwd=2, col=3)
lines(2010:2019,fore$pred - 1.96*fore$se, lty=2, lwd=2, col=3)

Q3.41

plot(unemp);acf(unemp);pacf(unemp);plot(diff(unemp)); 

acf(diff(unemp));pacf(diff(unemp));

fit=auto.arima(unemp,d=1)
fit

Series: unemp 
ARIMA(2,1,0)(2,1,1)[12] 

Coefficients:
         ar1     ar2     sar1     sar2     sma1
      0.1448  0.2317  -0.1792  -0.1140  -0.5569
s.e.  0.0519  0.0527   0.1104   0.0873   0.1016

sigma^2 estimated as 452.4:  log likelihood=-1608.57
AIC=3229.14   AICc=3229.38   BIC=3252.44

fore=forecast(fit,12)
plot( window(unemp, start=c(1975,1), end=c(1978,12)), type='o', pch=16,
      lwd=2, xlim=c(1975,1980), ylim=c(300,900), ylab='unemp')
lines(fore$mean, type='o', pch=16, col=2, lwd=2)

lines(ts(fore$lower[,2],start=c(1979,1),freq=12), lty=2, lwd=2, col=3)
lines(ts(fore$upper[,2],start=c(1979,1),freq=12), lty=2, lwd=2, col=3)

arma.fit=auto.arima(log(jj)) 
arma.fit

Series: log(jj) 
ARIMA(2,0,0)(1,1,0)[4] with drift 

Coefficients:
         ar1     ar2     sar1   drift
      0.2686  0.2855  -0.2695  0.0382
s.e.  0.1137  0.1214   0.1212  0.0042

sigma^2 estimated as 0.007793:  log likelihood=82.47
AIC=-154.95   AICc=-154.14   BIC=-143.04

Dljj=diff(log(jj), lag=4) 
plot(Dljj); acf(Dljj); pacf(Dljj)

sarima( log(jj), 2,0,0,0,1,0,4)

initial  value -2.421271 
iter   2 value -2.471452
iter   3 value -2.481685
iter   4 value -2.481768
iter   5 value -2.481772
iter   6 value -2.481773
iter   6 value -2.481773
iter   6 value -2.481773
final  value -2.481773 
converged
initial  value -2.418235 
iter   2 value -2.420437
iter   3 value -2.420994
iter   4 value -2.421016
iter   5 value -2.421016
iter   6 value -2.421016
iter   6 value -2.421016
iter   6 value -2.421016
final  value -2.421016 
converged
$fit

Call:
stats::arima(x = xdata, order = c(p, d, q), seasonal = list(order = c(P, D, 
    Q), period = S), xreg = constant, transform.pars = trans, fixed = fixed, 
    optim.control = list(trace = trc, REPORT = 1, reltol = tol))

Coefficients:
         ar1     ar2  constant
      0.2609  0.1887    0.0381
s.e.  0.1165  0.1171    0.0045

sigma^2 estimated as 0.007873:  log likelihood = 80.17,  aic = -152.33

$degrees_of_freedom
[1] 77

$ttable
         Estimate     SE t.value p.value
ar1        0.2609 0.1165  2.2398  0.0280
ar2        0.1887 0.1171  1.6116  0.1111
constant   0.0381 0.0045  8.5138  0.0000

$AIC
[1] -1.835331

$AICc
[1] -1.831671

$BIC
[1] -1.720534

fore = sarima.for( log(jj), n.ahead=4, 2,0,0,1,1,0,4)

plot( window(jj, start=c(1975,1), end=c(1980,4)), type='o', pch=16,
      lwd=2, xlim=c(1974,1982), ylim=c(5, 23), ylab='jj')
lines(1981+c(0:3)/4,exp(fore$pred), type='o', pch=16, col=2)

lines(1981+c(0:3)/4,exp(fore$pred + 1.96*fore$se), lty=2, lwd=2, col=3)
lines(1981+c(0:3)/4,exp(fore$pred - 1.96*fore$se), lty=2, lwd=2, col=3)

plot( window(jj, start=c(1975,1), end=c(1980,4)), type='o', pch=16,
      lwd=2, xlim=c(1974,1982), ylim=c(5, 23), ylab='jj')
lines(1981+c(0:3)/4,exp(fore$pred), type='o', pch=16, col=2)

lines(1981+c(0:3)/4,exp(fore$pred + 1.96*fore$se), lty=2, lwd=2, col=3)
lines(1981+c(0:3)/4,exp(fore$pred - 1.96*fore$se), lty=2, lwd=2, col=3)

X=cbind(rec,soi)
plot(X, main="")
acf(X,lag=100)

library(vars) 

VARselect(X,lag.max=20) #best AIC @ lag p=15
out=VAR(X,15) 
summary(out)

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